----- The following copyright 1991 by Dirk Terrell
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 Lecture #7 "The Stellar Rosetta Stone"

   Last time we looked at stellar temperatures and spectral types, and found 
that the color of a star indicates its surface temperature. Another 
important property of a star is its brightness, but we have to be sure we 
know what we mean when we refer to a star's brightness. Here's an example: 
which is brighter a penlite flashlight or a car headlight? Well, let's see, 
it must be obvious that a headlight is brighter than a flashlight, right? 
Suppose the flashlight is an inch from your eye and the car headlight is 50 
miles away. Which one is brighter? The flashlight of course! Wait a minute, 
we have concluded that both of them are brighter! Our dilemma lies in the 
fact that we are calling two different things 'brightness'. In the first 
example, we were referring to the total amount of light (energy) was put out 
by the two lights and we correctly concluded that the headlight put out 
light than the flashlight. In the second example we were referring to how 
bright the lights appeared to be and since the headlight was very far away, 
it LOOKED dimmer than the flashlight. Let's define the 'brightness' in the 
first case as the absolute brightness and the 'brightness' in the second as 
the apparent brightness. For stars, we measure brightnesses in units called 
magnitudes, with a smaller magnitude meaning a brighter star (i.e. a star of 
first magnitude is brighter than a second magnitude star). Thus we refer to 
a star's absolute brightness as its absolute magnitude. We can also measure 
a star's absolute brightness by the amount of energy it gives off each 
second and this is called its luminosity. We refer to a star's apparent 
brightness by its apparent magnitude. The difference between absolute and 
apparent magnitude, as the above examples illustrate, lies in the distance 
to the star. A star that appears dim could be a faint star that is close to 
us or a bright star that is very far away. The way absolute magnitude is 
defined is that it's the apparent magnitude a star would have if it were 10 
parsecs away (a parsec is approximately 3.26 light years). Also, an 
important rule to remember is that a difference of five magnitudes 
corresponds to a brightness ratio of 100. A first magnitude star is 100 
times brighter than a sixth magnitude star.

   Now, intuitively we might expect a relationship between the surface 
temperature of a star and its absolute brightness or luminosity, namely that 
hotter stars will be brighter. The way to see if this is actually the case 
is to make a graph of luminosity versus temperature for stars of various 
temperatures. At the beginning of this century, Danish astronomer Ejnar 
Hertzsprung and American astronomer Henry Norris Russell recognized this 
relationship and a plot of luminosity versus temperature is now called the 
Hertzsprung-Russell (HR) diagram. You will also hear HR diagrams called 
color-magnitude diagrams. Do you know why? When you see an HR diagram, 
indeed the hot stars have higher luminosities. One word about HR diagrams: 
for some reason, unbeknownst to me, temperature(which is on the x-axis) is 
plotted increasing to the left which is contrary to the way we usually do 
things, so that stars to the left of other stars in the diagram are hotter 
than the ones to the right. 

   When you plot the positions of stars in the HR diagram, one thing 
immediately becomes clear: most of the stars lie along a curve from the 
lower right to the upper left corners. This band of stars is known as the 
main sequence. It looks like this

  (bright) | *
       l   |  * * m
       u   |    * * a
       m   |      * * i
       i   |        * * n
       n   |          * *  
       o   |            * * s
       s   |              * * e
       i   |                * * q
       t   |                  * * n
       y   |                    * * c
  (dim)    |                      * * e
           -----------------------------
          (hot)   temperature     (cool)

   As we will see, the HR diagram turns out to be a very powerful tool in 
understanding the structure and evolution of stars. The HR diagram enables 
us to test our theories of stellar evolution by creating an HR diagram for 
our theoretical models that can be directly compared to observed HR 
diagrams. One nice example of such a test is to compute structural models of 
stars assuming that the chemical composition of the star is always uniform 
throughout the star but slowly changes from 90% hydrogen/10% helium to 10% 
hydrogen/90% helium. When you do this the model will give you the luminosity 
and effective temperature of the star. For the uniform case, the model 
predicts that the star's temperature will rise (i.e. it will move to the 
left in the HR diagram as it evolves). But observed HR diagrams show that 
stars move to the RIGHT as they evolve (they become cooler). So, that means 
that stars do not maintain a uniform chemical compostion as they evolve. We 
understand this as the result of nuclear fusion that takes place in the core 
of the star. In the core hydrogen is converted to helium, but in the 
envelope (outer layers) of the star, the temperature and density are too low 
for fusion to take place and the chemical composition remains constant. So 
over time the star's chemical composition becomes non-uniform. When we 
compute structural models with proper nuclear fusion calculations, we find 
that the models predict that the star will move to the right in the HR 
diagram, which is what we observe in real stars.